Hey, another math question

Mathematics

1 answer:

Lena [83]3 years ago

3 0

Answer:

Step-by-step explanation:

By adjacent interior angles theorem,

If a transversal line 'r' intersects two parallel lines 'm' and 'n' then the consecutive interior angles are supplementary.

a° + (3x - 18)° = 180°

a° = 180° - (3x - 18)°

By vertical angles theorem,

If two straight lines intersect each other at a point, opposite angles formed are equal in measure.

180° - (3x - 18)° = (5x - 10)°

(5x - 10) + (3x - 18) = 180

(5x + 3x) - (10 + 18) = 180

8x - 28 = 180

8x = 180 + 28

8x = 208

x = 26

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W(t)W, left parenthesis, t, right parenthesis models the daily water level (in \text{cm}cmstart text, c, m, end text) at a pond

erastovalidia [21]

Answer:

t=152 days (in radians)

Step-by-step explanation:

W(t)models the daily water level at a pond in Arizona, t days after the hottest day of the year. (t is entered in radian)

$W(t) = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43$

We want to determine the first time,t at which the water level is 30cm.

When W(t)=30

$30 = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43\\30-43=15\cos\left(\dfrac{2\pi}{365}t\right)\\-13=15\cos\left(\dfrac{2\pi}{365}t\right)\\-\dfrac{13}{15} =\cos\left(\dfrac{2\pi}{365}t\right)\\cos^{-1}(-\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)\\cos^{-1}(\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)$

$cos^{-1}(\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)\\t=\dfrac{365}{2\pi}\cdot cos^{-1}(\dfrac{13}{15})\\t=152.16\\\approx 152 days \text{ (to the nearest whole day)}$

6 0

3 years ago

Read 2 more answers

Solve the inequality (question 30 please, already solved others)

STALIN [3.7K]

$\bf \cfrac{1}{4}n+12 \geqslant \cfrac{3}{4}n-4\implies \cfrac{1}{4}n+16 \geqslant \cfrac{3}{4}n\implies 16\geqslant \cfrac{3n}{4}-\cfrac{1n}{4}\implies 16\geqslant \cfrac{3n-1n}{4} \\\\\\ 16\geqslant\cfrac{2n}{4}\implies 16\geqslant \cfrac{n}{2}\implies 32 \geqslant n$