Notice that 4\(\displaystyle\sqrt{{4}}{<}\sqrt{{5}}{<}\sqrt{{9}}\to{2}{<}\sqrt{{5}}{<}{3}\)</span>

Question

asked 2021-05-06

Two uniformly charged spheres are firmly fastened to andelectrically insulated from frictionless pucks on an airtable. The charge on sphere 2 is three times the charge onsphere 1. Draw the force diagram that correctly showsthe magnitude and direction of the electrostatic forces. Explain your reasoning.

asked 2020-12-17

The square root of a number is between 7 and 8. Which could be the number? *

asked 2020-12-12

Which of the following is/are always false ?

(a) A quadratic equation with rational coefficients has zero or two irrational roots.

(b) A quadratic equation with real coefficients has zero or two non - real roots

(c) A quadratic equation with irrational coefficients has zero or two rational roots.

(d) A quadratic equation with integer coefficients has zero or two irrational roots.

(a) A quadratic equation with rational coefficients has zero or two irrational roots.

(b) A quadratic equation with real coefficients has zero or two non - real roots

(c) A quadratic equation with irrational coefficients has zero or two rational roots.

(d) A quadratic equation with integer coefficients has zero or two irrational roots.

asked 2021-01-05

Consider the polynomial \(\displaystyle{f{{\left({X}\right)}}}={x}^{{4}}+{1}\)

a) Explain why f has no real roots, and why this means f mustfactor as a product of two ireducible quadratics.

b) Factor f and find all of its complex roots.

a) Explain why f has no real roots, and why this means f mustfactor as a product of two ireducible quadratics.

b) Factor f and find all of its complex roots.

asked 2021-02-27

The table to the right has the inputs, x, and the outputs for three functions, f, g, and h. Use second differences to determine which function is exactly quadratic, which is approximately quadratic, and which is not quadratic.

The functon

f(x) is _______ quadratic,

g(x) is _____ quadratic,

h(x) is _______ quadratic.

The functon

f(x) is _______ quadratic,

g(x) is _____ quadratic,

h(x) is _______ quadratic.

asked 2021-01-24

You have been asked to bake the birthday cake of a little girl who is about to turn three. When looking up suggestions online on how to bake this cake, you found that most everyone suggests baking the cake in smaller circular cake pans that have a diameter of 6 inches. That’s the best way to get the height for the unicorn head. A normal circular cake pan (and the only kind you have) has a diameter of 9 inches. You need to buy cake pans. As an experienced baker, you know that the recipe you are planning on using usually fills two regular (9-inch) cake pans, with a little room to spare. How many 6-inch pans do you need to buy? (We’re going to assume that all cake pans are the same height.)

asked 2021-03-26

A 1200kg pick up truck traveling south at 15m/s collides witha 750kg car traveling east. The two vehicles stick together. Thefinal position of the wreckage after the collision is 25m, atan angle of 50 south of east, from the point of impact. If thecoefficient of friction between the tires and the road, from thelocation of the collision to the point at which the wreckage comesto rest is 0.4, what was the speed of the car just before thecollision?

asked 2021-05-18

The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance \(\displaystyle{R}_{{x}}\) is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance \(\displaystyle{R}_{{y}}\). The procedure for finding the unknown resistance \(\displaystyle{R}_{{x}}\) is as follows. Measure resistance \(\displaystyle{R}_{{1}}\) between points A and B. Then connect A and B with a heavy conducting wire and measure resistance \(\displaystyle{R}_{{2}}\) between points A and C.Derive a formula for \(\displaystyle{R}_{{x}}\) in terms of the observable resistances \(\displaystyle{R}_{{1}}\) and \(\displaystyle{R}_{{2}}\). A satisfactory ground resistance would be \(\displaystyle{R}_{{x}}{<}{2.0}\) Ohms. Is the grounding of the station adequate if measurments give \(\displaystyle{R}_{{1}}={13}{O}{h}{m}{s}\) and R_2=6.0 Ohms?

asked 2021-01-22

Explain how to complete the square for an expression of the form x²+bx.

Add __ to \(\displaystyle{x}²+{b}{x}.\)

Add __ to \(\displaystyle{x}²+{b}{x}.\)

asked 2021-01-19

Sample of two different models of cars were selected, and the actual speed for each car was
determined when the speedometer registered 50 mph. The resulting 95% confidence intervals
for mean actual speed were (50.3, 52.7) and (49.8, 50.6) respectively. Assuming that the two
sample standard deviations are equal, which confidence interval is based on the larger sample
size? Explain your reasoning.