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3 years ago

Saturday the low temperature was 56°F and the high temperature was 60° higher what was the high temperature on Saturday

Mathematics

1 answer:

leva [86]3 years ago

4 0

116 degrees. It’s simple.

56 is what the low was, but the high was 60 more.
Therefore,
56+60=116

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8 times what equals 40

erica [24]

Eight times five equals forty.

The answer is 5.

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3 years ago

Read 2 more answers

A road has a 10% grade, meaning increasing 1 unit of rise to every 10 units of run.

fenix001 [56]

The grade is the ratio of rise to run, i.e. the slope aka the tangent.

$\tan \theta = \dfrac{1}{10}$

$\theta = \arctan 0.1 \approx 5.711^\circ$

Answer: (a) 6 degrees

For part b, the road is the hypotenuse c of a right triangle whose tangent of the small angle is 1/10. The height h or rise is the side opposite the small angle.

$\sin\theta = \dfrac h c$

$h = c \sin \theta$

We could just take the sine of the angle we got but let's get it from the tangent exactly.

$\cos^2 \theta + \sin ^2 \theta = 1$

Dividing by squared cosine

$1 + \tan ^2 \theta = 1/\cos^2 \theta = 1/(1- \sin^2 \theta)$

$(1- \sin^2 \theta) = 1/(1 + \tan^2 \theta)$

$\sin^2 \theta = 1 - 1/(1 + \tan^2 \theta)$

$\sin^2 \theta = 1 - 1/(1 + (1/10)^2) = 1-1/(101/100) = 1/101$

$h = c \sin \theta = 2 \sqrt{1/101} \approx 0.199$

Answer: (b) Rise of 0.199 km

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3 years ago

What is the length of segment AB with point A and B located at (-4, 1) and (2, 9)

navik [9.2K]

Answer:

<h3>The answer is 10 units</h3>

Step-by-step explanation:

The distance between two points or a line segment can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 1) and (2, 9)

The length of segment AB is

$|AB| = \sqrt{ ({ - 4 - 2})^{2} + ({1 - 9})^{2} } \\ = \sqrt{( { - 6})^{2} + ({ - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} \: \: \: \: \: \: \: \: \\ = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$